The operating efficiency of industrial and domestic systems largely depends on cleanliness of their surfaces exposed to process fluids and subjected to natural or induced heat transfer and electrochemical conditions. Untreated process fluids contain a number of constituents the solubility of which can substantially decrease in certain temperature and pH ranges resulting in scaling or precipitation on the surface of an apparatus or a vessel. These processes, otherwise known as fouling, impede the proper flow of heat through the equipment surfaces, which leads to an overall decrease of the system operating efficiency.
Further, in a system where the fluid or liquid is flowing or being pumped, the formation of scales and deposits decreases the diameter of passages, increases the flow resistance and mechanical stresses thereby increasing the risk of structural damage as well as energy costs. Also, the formation of scales and deposits on metal surface favors localized and under deposit corrosion, thereby reducing the operating lifetime of the equipment.
Fouling can be a function of many factors: liquid temperature and chemistry; physical characteristics of the flow such as Reynolds number, shear stress and viscosity; geometry of the equipment; materials of construction; and temperature of the heat transfer surface. The most important liquid characteristics are the level of dissolved solids, the presence of microbiological matter and the process chemistry. Liquid velocity, shear stress and viscosity are the determinant flow characteristics.
Induced fouling deposits can form on surfaces that are either colder or warmer than the temperature of the bulk liquid. For example, in industrial processes employing water-cooled heat exchangers, silicate scale deposits can form on surfaces that are colder than the bulk water while carbonate and sulfate deposits can form on surfaces warmer than the bulk water. Another example of fouling of a colder surface is the formation of ice from water or the solidification of wax laden hydrocarbons while transporting fluids containing these substances in pipelines exposed to low temperatures.
Further, an electrochemical polarization in the form of potential or current naturally or intentionally applied to a heat transfer surface may significantly affect fouling due to the electrochemical reactions induced at the equipment surface. For example, the surface pH increase induced electrochemically by corrosion results in the increase of the deposition rate of calcium carbonate scale on a mild steel heat exchange surface compared to that made of stainless steel. Corrosion results in the formation of anodic and cathodic sites on mild steel surface immersed in water at ambient conditions. Reduction at the cathodic sites of the oxygen dissolved in water leads to a near surface pH increase that favors precipitation of carbonate scales. In another example mild steel industrial heat exchangers are often protected against corrosion using cathodic polarization using sacrificial anodes or imposed current. A commonly accepted cathodic protection criterion for mild steel parts is the application of a negative potential which results in the increase of the near surface pH which favors carbonate scaling. The use of two or more different metals in constructing a heat exchanger can subject one of them to a positive potential sufficiently high to result in water oxidation which produces a near-surface excess of H.sup.+ ions, and thus, a pH decrease will occur resulting in the scale dissolution.
The decrease of the heat exchange at a surface due to fouling is defined by the fouling thermal resistance, R.sub.f as: EQU R.sub.f =1/U.sub.fouled -1/U.sub.clean (1)
where 1/U.sub.clean and 1/U.sub.fouled are the heat transfer coefficients of the surface in clean and fouled conditions, respectively. The heat transfer coefficients are defined as: EQU T.sub.wall clean -T.sub.bulk =1/U.sub.clean (Q/A) (2a) EQU T.sub.wall fouled -T.sub.bulk =1/U.sub.fouled (Q/A) (2b)
where T.sub.wall clean and T.sub.wall fouled are the temperatures of the surface in clean and fouled conditions, respectively; T.sub.bulk is the bulk temperature of the process fluid; Q/A is the heat flux through the heat exchange surface having area A.
Thus, the fouling resistance may be determined by measuring the change of heat transfer through a given surface over time.
As shown in Equations 2a and 2b above, the measurement of fouling resistance requires the knowledge of the heat transfer resistance of the same surface at clean conditions. This brings unavoidable uncertainty because the heat transfer resistance of a clean surface depends on the thermal resistance of the clean surface itself, R.sub.wall, and the thermal resistance of the process fluid, R.sub.fluid : EQU 1/U.sub.clean =R.sub.wall +R.sub.fluid (3a)
combining equations (1) and (3a): EQU 1/U.sub.fouled =R.sub.f +R.sub.wall +R.sub.fluid (3b)
The thermal resistance of the fluid is highly dependent upon the fluid flow rate as shown in Equation 4 below: EQU 1/U.sub.clean =R.sub.wall +C/V.sup.n (4)
where C is the constant, V is the velocity of the fluid and R.sub.wall, C and n can be obtained through calibration of the heater.
Measurements as described above may result in artificially low or even negative values of thermal resistance during the initial operating period. This happens due to the initial deposits increasing the roughness of the heat exchange surface which consequently decreases surface-to-fluid thermal resistance. As a result, the actual increase in thermal fouling resistance may not be detected. As reported by J. Knudsen, "Apparatus and Technologies for Measurement of Fouling of Heat Transfer Surfaces, and Fouling of Heat Transfer Equipment", Proceedings of an International Conference, Rensselaer Polytechnic Institute, pp. 57-82 (1979), as the fouling layer thickens, the effect of the lower thermal conductivity dominates the improved local heat transfer coefficient due to roughening and the fouling resistance again becomes positive. Therefore, the common heat transfer resistance measurements have a minimal fouling limit below which they cannot reliably detect or determine R.sub.f. This presents a substantial obstacle especially when effective anti-fouling treatments are being screened or tested.
Although important from the technical standpoint, the measurement of fouling thermal resistance does not provide a strict quantitative answer as to how a certain treatment affects the deposition mass rate of the fouling deposit. This deposition mass rate represents the velocity of mass accumulation of fouling deposit per square unit of area per unit of time and is expressed as follows: EQU m.sub.f =R.sub.f (.rho..sub.f k.sub.f) (5)
wherein m.sub.f is the deposit mass per unit area per unit of time; R.sub.f is the thermal fouling resistance; .rho..sub.f is the density of the fouling deposit; and k.sub.f is the thermal conductivity of the fouling deposit.
Traditionally, coupons or forensic investigation were used to determine m.sub.f, the mass of deposit on the scaled surface. However, the employment of a piezoelectric microbalance makes this task relatively easy to accomplish in real time and in situ. The principle of piezoelectric mass measurement is based upon the property of a quartz resonator to change its mechanical resonance frequency fo proportionally to the mass and viscoelastic properties of the deposited material. U.S. Pat. No. 5,201,215 discloses a method for the simultaneous measurement of the mass loading and fluid property changes using such a quartz crystal microbalance apparatus. The change in frequency is expressed as follows: ##EQU1##
where f.sub.0 is the unperturbed resonant frequency of the quartz crystal; N is the harmonic number; .mu..sub..mu. is the quartz shear stiffness, .rho..sub.q is the density of quartz; .rho..sub.s is the surface mass density of the deposit (mass/area), .rho. is the density of the medium contacting the resonator and .eta. is the viscosity of the medium contacting the resonator.
Those skilled in the art use electronic circuit analysis methods to determine the separate contributions from the mass and viscoelasticity of the deposit. Also known are equations used for thick deposits when the change of resonant frequency is higher than 10%. However, in the case of a crystalline non-viscous deposit when the change is less than 10% (which corresponds to approx. 8900 .mu.g/cm.sup.2, or 32 micron layer of calcium carbonate with the density of 2.76 g/cm3) a simplified expression can be used: EQU .rho..sub.s =-C.DELTA.f.sub.0 (7)
where C is determined by calibration and is typically equal to 1.77.times.10.sup.-2 .mu.g/(sec cm.sup.2 Hz) for a 5 MHz quartz crystal.
The use of a piezoelectric microbalance allows the measurement of the effects of electrochemical or chemical reactions on the formation of the scale or deposit on the electrode disposed on the quartz crystal surface. See European Patent Application No. 676 637 A1.
Although useful for comparing the effect of antifouling treatments, electrochemical methods do not simulate a heat exchange surface and form deposits with morphology different than those caused by heat transfer. Electrochemical methods rely upon the precipitation of scale deposits driven solely by the electrolysis of the water solutions and without any contemplation of the chemical effect of the heat transfer. The scale precipitation is driven by the electrochemical reduction of dissolved oxygen and water in the range of -1 V versus saturated calomel electrode (SCE), which results in a pH increase near the electrode. This is limited in that some process streams may not contain dissolved oxygen or water and some forms of fouling may not be driven by a pH increase near the electrode. Further, the accuracy of the electrochemical methods may be affected by the electrochemical reduction of other solution species such as nitrates. The electrochemical methods are based upon the effect of polarization with a definite sign and magnitude. In this way they can not provide data on how scaling is affected by an electrochemical polarization applied beyond the specified limits.
Further, piezoelectric probes become fouled during the tests and typically must be removed from the solution for cleaning. As a result, testing procedures are delayed and are therefore more costly. Surprisingly enough the prior art does not teach us a suitable in-situ method of cleaning.
Therefore, there is a need for a precision method that can measure the mass rate of a fouling reaction that is driven by the supply or withdrawal of heat (to or from the fluid) through the surface subjected to electrochemical polarization. The precision of the method should be as high as it is given by the use of a piezoelectric microbalance. The exploration of the effect of electrochemical polarization should be allowed in the entire cathodic or anodic range so as to simulate the polarization naturally occurring or artificially induced in the industrial equipment. Further, there is a need that the method would allow consecutive measurements without the need to withdraw the probe surface from the liquid being tested or dismantling the testing apparatus, and without the use of additional chemicals. It is also desirable that the probe cleaning could be done electrochemically under the condition that the material of the sensor electrode is not degraded by the cleaning. It is also desirable that the probe cleaning could also be done by communication to the fouling deposit of a certain heat flux in direction opposite to that caused the formation of the deposit.